Week 5 Study Guide — Dynamic Systems and Uniform Circular Motion

Directly supported by notes

These are explicitly named in the lecture slides, handwritten notes, or Tutorial 5 PDFs.

Topic	Direct source coverage
Newton’s three laws	Slide 14; restated in every worked example
Free body diagram workflow	Slide 13 (Identify → Define → Model → Represent)
Common forces (weight, normal, tension, spring, friction)	Slide 12; used in Examples 1–4
Friction force, static vs kinetic	Slide 12; sliding test in Example 2
Coupled blocks + spring	Example 1, slide 16; both system and separate-FBD methods in notes p. 2
Incline + friction	Example 2, slide 17; notes pp. 3–4
Vertical circle (tension at top/bottom)	Example 3, slide 25; notes p. 5
Conical pendulum (horizontal circle)	Example 4, slide 26; notes p. 6
Banked curves (no friction)	Slide 23
Tutorial problems 1–6	Tutorial 5.pdf and Tutorial 5_Solutions.pdf

The workshop expects you to be able to:

1. Draw a clean FBD with labelled forces and a coordinate system on any body in any of the standard set-ups.
2. Translate that FBD into $\sum F_x=m{a}_x$ and $\sum F_y=m{a}_y$.
3. Resolve weight on an incline into $mg\sin \theta$ (along slope) and $mg\cos \theta$ (perpendicular).
4. Decide whether an object slides or stays put using the $\tan \theta$ vs ${\mu }_s$ comparison.
5. Recognise that the net inward force on a circling body equals $m{v}^2/r$, and project the real forces onto the radial direction to get the governing equation.

Strongly inferred from workshop materials

The lecture (slide PDF only partially parseable here) almost certainly covers, in this order:

• Study-skills opener (slides 3–9): daily check-ins, Rule of 3, Pomodoro Sprint (2 + 25 + 5), 4-Pom Rule, “Stop the Line”, break hygiene.
• Problem-solving framework (slide 10): Model → Visualise → Solve → Assess, with the lecturer’s emphasis to spend most time on Visualise.
• Common forces and the friction formula (slide 12).
• FBD workflow (slide 13).
• Newton’s laws (slide 14) and an analysis approach (slide 15).
• Example 1 — coupled blocks with a spring (slide 16).
• Example 2 — block on a 30° incline with friction (slide 17).
• Definition of uniform circular motion (slide 19).
• Centripetal acceleration and force (slides 20–21).
• Conical pendulum (slide 22) and banked curves (slide 23).
• Cautions for circular motion: centripetal is the net force; constant speed ≠ constant velocity; pick “toward centre” as positive (slide 24).
• Example 3 (vertical circle) and Example 4 (conical pendulum).

Possible lecture content (not in notes)

May appear in the lecture but is not explicit in the materials I have:

• Vertical circular motion at non-extreme positions (side of the loop).
• Minimum speed to maintain contact at the top of a vertical loop ($T=0$ condition $\Rightarrow v_{\min }=\sqrt{gr}$).
• Banked curves with friction (combined $F_N$ and $F_{fric}$ supplying centripetal force).
• Apparent weight in a vertically accelerating reference frame.
• The relationship between period $T$ and angular speed $\omega$ for circular motion.

Gaps requiring official source check

• Whether the assessment uses the angle-from-horizontal convention everywhere, or sometimes from the vertical. Tutorial Ex. 4 and lecture Example 4 use horizontal; confirm with your tutor.
• Whether the Pomodoro/study-workflow content is examinable (likely not, but listed in lecture).
• The value of $g$ used in marking: the lecture and Tutorial 5 use $g=9.8$ m/s${}^2$, not $9.81$.

Worked examples

Three notes cover the topic at increasing depth:

• Lecture summary — every formula and worked example in lecture order, with slide references.
• Cheatsheet — fast revision tables, recipes, and the quiz (mixed difficulty).
• In-depth analysis — the why behind each technique, the derivation of $a_c=v^2/r$, the two-stage sliding test, and a complete exam-style sample.

Common mistakes

• Adding a centripetal force arrow to the FBD. Centripetal force is the net of real forces resolved inward, not an extra force.
• Confusing constant speed with constant velocity. Uniform circular motion has changing direction, so $\vec{a}\ne 0$.
• Wrong angle convention on the conical pendulum. In this course $\theta$ is measured from the horizontal, so $r=L\cos \theta$.
• Skipping the sliding test on an incline. Compare ${\mu }_s$ with $\tan \theta$ before assuming kinetic friction applies.
• Treating a negative $\mu$ as meaningful. $\mu$ is always positive by definition. A negative sign in your algebra means you drew friction the wrong way on the FBD.
• Forgetting unit conversion. km/h $\to$ m/s by dividing by 3.6 before plugging into $a_c$.
• Spring problems with circular motion: the orbit radius $R$ is natural length plus extension, so spring force is $k(R-x_0)$, not $kR$.
• Drawing only one FBD for a two-body system when you need the internal force.

Practice questions

Tutorial 5 (Wolfson Ch. 4 & 5). Recommended order for a first pass:

• FBD warm-up: Exercise 1 (three blocks on a frictionless surface, contact forces).
• Friction: Exercise 2 (sled at constant speed, find $\mu$); Exercise 5 (unbanked turn, find required $\mu$).
• Incline with friction: Exercise 3 (crate on 30° ramp held by a rope over a pulley, with weight $w$).
• Circular motion: Exercise 4 (rock on a string, breaking-tension limit); Exercise 6 (spring providing centripetal force — challenge).

Re-do Example 1 (spring-coupled blocks) by both methods (system and separate FBDs) — that builds the intuition for every two-body problem in the course.

Assessment relevance

• Coupled-body FBDs and uniform circular motion appear on virtually every paper.
• Banked curves and conical pendulums are very common.
• The portfolio expects neat, labelled FBDs with explicit coordinate axes — practice this in every tutorial because marks are awarded for the diagram itself, not just the final number.

Confidence report

• Directly supported: every formula listed in the cheatsheet and every worked example, all of which are in the slides, the handwritten notes, or Tutorial 5_Solutions.pdf.
• Inferred: the lecture’s exact ordering (re-built from slide numbers in the lecture summary), and the choice of which study-skills content to emphasise.
• Gap: vertical-loop minimum-speed condition, banked-curve-with-friction, and period/angular-speed relations — likely tutored later in the course but not in Week 5 materials.

Source files used

• EGD102-Physics/Lecture5_CTP1-1.pdf
• EGD102-Physics/EGD102 - Lecture5 - Notes.pdf
• EGD102-Physics/Tutorial 5.pdf
• EGD102-Physics/Tutorial 5_Solutions.pdf